Video Transcript
A galvanometer is connected to an alternating current source that has a low frequency. Terminal 𝑎 of the galvanometer is positive when terminal 𝑏 is negative and vice versa. The polarities of the terminals alternate periodically. Which of the following most correctly describes the deflection of the galvanometer arm? (A) The arm remains at the zero-deflection position. (B) The arm undergoes uniform circular motion. (C) The arm oscillates between two positions, one of which is the zero-deflection position. (D) The arm oscillates between two positions equidistant from the zero-deflection position.
The diagram that we’re given shows the inner workings of a galvanometer, which in a circuit diagram is symbolized by a circle with a 𝐺 in it. The way that it works is that when current passes through the galvanometer, it induces a magnetic field that interacts with the already-present magnetic field between the two permanent magnets. This creates a force on the wires in between these permanent magnets, causing them to rotate in one direction or another, which causes a subsequent deflection of the needle in one direction or the other. Greater values of current will induce a more powerful magnetic field, which will create more force on the wire, which will cause a greater deflection of the needle on the dial. And in this way, a galvanometer is able to measure the magnitude of the current passing through it.
The direction of the current through the wires also determines the direction of the deflection of the needle. However, galvanometers are pretty sensitive, and you can usually only measure small currents with them before the needle gets maxed out. However, there is a work-around. By connecting a resistor with a very small resistance in parallel with the galvanometer, we can increase the effective current we can measure before the needle arm maxes out its deflection. When used in this way, such a resistor is called a shunt resistor. But no matter the value of the current or the resistance of the shunt resistor, the needle arm will not deflect past the maximum points on the dial.
Knowing this, we would have to say that answer (B) is not correct. The needle arm cannot undergo uniform circular motion because the coils of wire at either end of the galvanometer would prevent the needle from deflecting past a certain point. In order for the needle arm to undergo uniform circular motion, we would have to have a very broken galvanometer. Answer (B) is not correct. Looking at all of the other answers that we have left, it becomes quite apparent why galvanometers are only used to measure direct current because all of these answers sound terrible for actually trying to get a measurement. If the needle arm remains at the zero-deflection position even when there’s a current going through the galvanometer, it means it’s not reading anything and is essentially useless.
Meanwhile, if the arm oscillates between two different positions, like we see in answers (C) and (D), this is also bad, since a good measurement device ought to give you a nice stable number, not one that fluctuates between a range of values. So all of these answers are awful for giving us an actual measurement of current, but we’re just looking for the needle deflection. The question tells us that this galvanometer is connected to a low-frequency alternating current source and that the terminals 𝑎 and 𝑏 are always of opposite polarities. What this is going to look like is that all of the current will first be in one direction, which will cause the needle to deflect over to one side. So because the arm does not remain at the zero-deflection position, we already know that answer (A) cannot be correct.
Now clearing the incorrect answers (A) and (B), we can show a graph that shows how alternating current changes with time. The needle deflection is at its maximum when the current magnitude is at its maximum. But as the current magnitude in this direction decreases, so too will the needle deflection, eventually going back to zero. At the exact moment where there is no current in either direction, the needle arm will be pointing at zero, but it doesn’t stop there. The current direction will flip, and the needle arm will start deflecting to the other side, eventually reaching the maximum deflection in this direction at the maximum magnitude of the current in this direction. Before the current magnitude decreases, the needle arm deflects back to zero, and the whole process repeats.
Notably, these two maximum deflection positions of the needle arm are equidistant from the zero-deflection position because the maximum magnitude of this alternating current is the same for both directions. So even though the needle arm passes through the zero-deflection position, it is not one of the positions that the arm oscillates between. This means that the answer that most correctly describes the deflection of the needle is answer (D). The arm oscillates between two positions equidistant from the zero-deflection position.
